Question

In fig 8.17, $∆$XYZ is a right angled triangle and $\angle$XYZ = 90$°$ Write all trigonometric ratios of angle X and angle Z.

Answer 1

The trigonometric ratios of angle X are:

$$\begin{gathered} \sin \mathrm{X}=\frac{\mathrm{YZ}}{\mathrm{ZX}},\mathrm{cosec}\mathrm{X}=\frac{\mathrm{ZX}}{\mathrm{YZ}} \\ \cos \mathrm{X}=\frac{\mathrm{XY}}{\mathrm{ZX}},\sec \mathrm{X}=\frac{\mathrm{ZX}}{\mathrm{XY}} \\ \tan \mathrm{X}=\frac{\mathrm{YZ}}{\mathrm{XY}},\cot \mathrm{X}=\frac{\mathrm{XY}}{\mathrm{YZ}} \end{gathered}$$

The trigonometric ratios of angle Z are:

$$\begin{gathered} \sin \mathrm{Z}=\frac{\mathrm{XY}}{\mathrm{ZX}},\mathrm{cosec}\mathrm{Z}=\frac{\mathrm{ZX}}{\mathrm{XY}} \\ \cos \mathrm{Z}=\frac{\mathrm{YZ}}{\mathrm{ZX}},\sec \mathrm{Z}=\frac{\mathrm{ZX}}{\mathrm{YZ}} \\ \tan \mathrm{Z}=\frac{\mathrm{XY}}{\mathrm{YZ}},\cot \mathrm{Z}=\frac{\mathrm{YZ}}{\mathrm{XY}} \end{gathered}$$